**Problem Statement:**A box is initially sliding across a frictionless floor with a constant speed of 2.5 m/s. Then, the box encounters a rough surface and travels for 12 meters before coming to a stop. What is the coefficient of kinetic friction between the box and the rough surface? Use the work-energy theorem.**Solution Approach:**To find the coefficient of kinetic friction (\( \mu_k \)), we can use the work-energy theorem, which states that the work done by all forces acting on an object equals the change in its kinetic energy.**Given:**- Initial velocity (\( v_i \)) = 2.5 m/s- Final velocity (\( v_f \)) = 0 m/s (since the box comes to a stop)- Distance traveled on the rough surface (\( d \)) = 12 meters**Steps:**1. Calculate the initial kinetic energy using \( KE = \frac{1}{2}mv^2 \).2. Since the box stops, the final kinetic energy is 0.3. The work done by friction (\( W \)) equals the change in kinetic energy.4. Use the formula for work done by friction: \( W = -f_k \cdot d \), where \( f_k \) is the kinetic friction force.5. The friction force can be expressed as \( f_k = \mu_k \cdot N \), where \( N \) is the normal force. On a horizontal surface, \( N = mg \).6. Solve for \( \mu_k \) using the equation derived from the work-energy theorem and rearrange to find the desired coefficient of kinetic friction.**Note:**This solution involves calculating the work-energy transfer and applying Newton's laws of motion to find the relationship between the friction force and the normal force.

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Description: **Problem Statement:**A box is initially sliding across a frictionless floor with a constant speed of 2.5 m/s. Then, the box encounters a rough surface and travels for 12 meters before coming to a stop. What is the coefficient of kinetic friction be

According to the work energy theorem, Work done by the friction = change in kinetic energy

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A box is initially sliding across a frictionless floor with a constant speed of 2.5 m/s. Then, the box encounters a rough surface and travels for 12 meters before coming to a stop. What is the coefficient of kinetic friction between the box and rough surface? Use the work-energy theorem.

A box is initially sliding across a frictionless floor with a constant speed of 2.5 m/s. Then, the box encounters a rough surface and travels for 12 meters before coming to a stop. What is the coefficient of kinetic friction between the box and rough surface? Use the work-energy theorem.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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